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<div class="header">
  <div class="headertitle">
<div class="title">arch/ZVector/MathFunctions.h</div>  </div>
</div><!--header-->
<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2007 Julien Pommier</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">// Copyright (C) 2009 Gael Guennebaud &lt;gael.guennebaud@inria.fr&gt;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// Copyright (C) 2016 Konstantinos Margaritis &lt;markos@freevec.org&gt;</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160; </div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment">/* The sin, cos, exp, and log functions of this file come from</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="comment"> * Julien Pommier&#39;s sse math library: http://gruntthepeon.free.fr/ssemath/</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160; </div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="preprocessor">#ifndef EIGEN_MATH_FUNCTIONS_ZVECTOR_H</span></div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="preprocessor">#define EIGEN_MATH_FUNCTIONS_ZVECTOR_H</span></div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160; </div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="preprocessor">#include &quot;../../InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160; </div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160; </div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160; </div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="preprocessor">#if !defined(__ARCH__) || (defined(__ARCH__) &amp;&amp; __ARCH__ &gt;= 12)</span></div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4i(23, 23);</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160; </div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000);</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160; </div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;<span class="comment">/* the smallest non denormalized float number */</span></div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos,  0x00800000);</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_inf,     0xff800000); <span class="comment">// -1.f/0.f</span></div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_nan,     0xffffffff);</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;  </div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;<span class="comment">/* natural logarithm computed for 4 simultaneous float</span></div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;<span class="comment">  return NaN for x &lt;= 0</span></div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f);</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f);</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f);</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f);</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f);</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f);</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f);</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160; </div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(exp_hi,  88.3762626647950f);</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160; </div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160; </div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160; </div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(1 , 1.0);</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(2 , 2.0);</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(half, 0.5);</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160; </div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(exp_hi,  709.437);</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303);</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160; </div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160; </div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160; </div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160; </div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;<span class="keyword">static</span> EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160; </div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;<span class="keyword">template</span>&lt;&gt; EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;Packet2d pexp&lt;Packet2d&gt;(<span class="keyword">const</span> Packet2d&amp; _x)</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;{</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;  Packet2d x = _x;</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160; </div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;  Packet2d tmp, fx;</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;  Packet2l emm0;</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160; </div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;  <span class="comment">// clamp x</span></div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;  x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo);</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;  <span class="comment">/* express exp(x) as exp(g + n*log(2)) */</span></div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;  fx = pmadd(p2d_cephes_LOG2EF, x, p2d_half);</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160; </div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;  fx = vec_floor(fx);</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160; </div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;  tmp = pmul(fx, p2d_cephes_exp_C1);</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;  Packet2d z = pmul(fx, p2d_cephes_exp_C2);</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;  x = psub(x, tmp);</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;  x = psub(x, z);</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160; </div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;  Packet2d x2 = pmul(x,x);</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160; </div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;  Packet2d px = p2d_cephes_exp_p0;</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;  px = pmadd(px, x2, p2d_cephes_exp_p1);</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;  px = pmadd(px, x2, p2d_cephes_exp_p2);</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;  px = pmul (px, x);</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160; </div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;  Packet2d qx = p2d_cephes_exp_q0;</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;  qx = pmadd(qx, x2, p2d_cephes_exp_q1);</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;  qx = pmadd(qx, x2, p2d_cephes_exp_q2);</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;  qx = pmadd(qx, x2, p2d_cephes_exp_q3);</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160; </div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;  x = pdiv(px,psub(qx,px));</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;  x = pmadd(p2d_2,x,p2d_1);</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160; </div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;  <span class="comment">// build 2^n</span></div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;  emm0 = vec_ctsl(fx, 0);</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160; </div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;  <span class="keyword">static</span> <span class="keyword">const</span> Packet2l p2l_1023 = { 1023, 1023 };</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;  <span class="keyword">static</span> <span class="keyword">const</span> Packet2ul p2ul_52 = { 52, 52 };</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160; </div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;  emm0 = emm0 + p2l_1023;</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;  emm0 = emm0 &lt;&lt; reinterpret_cast&lt;Packet2l&gt;(p2ul_52);</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160; </div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;  <span class="comment">// Altivec&#39;s max &amp; min operators just drop silent NaNs. Check NaNs in </span></div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;  <span class="comment">// inputs and return them unmodified.</span></div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;  Packet2ul isnumber_mask = <span class="keyword">reinterpret_cast&lt;</span>Packet2ul<span class="keyword">&gt;</span>(vec_cmpeq(_x, _x));</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;  <span class="keywordflow">return</span> vec_sel(_x, pmax(pmul(x, <span class="keyword">reinterpret_cast&lt;</span>Packet2d<span class="keyword">&gt;</span>(emm0)), _x),</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;                 isnumber_mask);</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;}</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160; </div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;<span class="keyword">template</span>&lt;&gt; EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;Packet4f pexp&lt;Packet4f&gt;(<span class="keyword">const</span> Packet4f&amp; _x)</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;{</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;<span class="preprocessor">#if !defined(__ARCH__) || (defined(__ARCH__) &amp;&amp; __ARCH__ &gt;= 12)</span></div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;  Packet4f x = _x;</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160; </div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;  Packet4f tmp, fx;</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;  Packet4i emm0;</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160; </div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;  <span class="comment">// clamp x</span></div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;  x = pmax(pmin(x, p4f_exp_hi), p4f_exp_lo);</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160; </div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;  <span class="comment">// express exp(x) as exp(g + n*log(2))</span></div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;  fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half);</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160; </div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;  fx = pfloor(fx);</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160; </div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;  tmp = pmul(fx, p4f_cephes_exp_C1);</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;  Packet4f z = pmul(fx, p4f_cephes_exp_C2);</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;  x = psub(x, tmp);</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;  x = psub(x, z);</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160; </div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;  z = pmul(x,x);</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160; </div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;  Packet4f y = p4f_cephes_exp_p0;</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;  y = pmadd(y, x, p4f_cephes_exp_p1);</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;  y = pmadd(y, x, p4f_cephes_exp_p2);</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;  y = pmadd(y, x, p4f_cephes_exp_p3);</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;  y = pmadd(y, x, p4f_cephes_exp_p4);</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;  y = pmadd(y, x, p4f_cephes_exp_p5);</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;  y = pmadd(y, z, x);</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;  y = padd(y, p4f_1);</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160; </div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;  <span class="comment">// build 2^n</span></div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;  emm0 = (Packet4i){ (int)fx[0], (<span class="keywordtype">int</span>)fx[1], (int)fx[2], (<span class="keywordtype">int</span>)fx[3] };</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;  emm0 = emm0 + p4i_0x7f;</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;  emm0 = emm0 &lt;&lt; reinterpret_cast&lt;Packet4i&gt;(p4i_23);</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160; </div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;  <span class="keywordflow">return</span> pmax(pmul(y, <span class="keyword">reinterpret_cast&lt;</span>Packet4f<span class="keyword">&gt;</span>(emm0)), _x);</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;  Packet4f res;</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;  res.v4f[0] = pexp&lt;Packet2d&gt;(_x.v4f[0]);</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;  res.v4f[1] = pexp&lt;Packet2d&gt;(_x.v4f[1]);</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;  <span class="keywordflow">return</span> res;</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;}</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160; </div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;<span class="keyword">template</span>&lt;&gt; EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;Packet2d psqrt&lt;Packet2d&gt;(<span class="keyword">const</span> Packet2d&amp; x)</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;{</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;  <span class="keywordflow">return</span> vec_sqrt(x);</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;}</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160; </div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;<span class="keyword">template</span>&lt;&gt; EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;Packet4f psqrt&lt;Packet4f&gt;(<span class="keyword">const</span> Packet4f&amp; x)</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;{</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;  Packet4f res;</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;<span class="preprocessor">#if !defined(__ARCH__) || (defined(__ARCH__) &amp;&amp; __ARCH__ &gt;= 12)</span></div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;  res = vec_sqrt(x);</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;  res.v4f[0] = psqrt&lt;Packet2d&gt;(x.v4f[0]);</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;  res.v4f[1] = psqrt&lt;Packet2d&gt;(x.v4f[1]);</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;  <span class="keywordflow">return</span> res;</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;}</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160; </div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;<span class="keyword">template</span>&lt;&gt; EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;Packet2d prsqrt&lt;Packet2d&gt;(<span class="keyword">const</span> Packet2d&amp; x) {</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;  <span class="keywordflow">return</span> pset1&lt;Packet2d&gt;(1.0) / psqrt&lt;Packet2d&gt;(x);</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;}</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160; </div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;<span class="keyword">template</span>&lt;&gt; EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;Packet4f prsqrt&lt;Packet4f&gt;(<span class="keyword">const</span> Packet4f&amp; x) {</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;  Packet4f res;</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;<span class="preprocessor">#if !defined(__ARCH__) || (defined(__ARCH__) &amp;&amp; __ARCH__ &gt;= 12)</span></div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;  res = pset1&lt;Packet4f&gt;(1.0) / psqrt&lt;Packet4f&gt;(x);</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;  res.v4f[0] = prsqrt&lt;Packet2d&gt;(x.v4f[0]);</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;  res.v4f[1] = prsqrt&lt;Packet2d&gt;(x.v4f[1]);</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;  <span class="keywordflow">return</span> res;</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;}</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160; </div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;<span class="comment">// Hyperbolic Tangent function.</span></div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;ptanh&lt;Packet4f&gt;(<span class="keyword">const</span> Packet4f&amp; x) {</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;  <span class="keywordflow">return</span> internal::generic_fast_tanh_float(x);</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;}</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160; </div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;}  <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160; </div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;}  <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160; </div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;<span class="preprocessor">#endif  </span><span class="comment">// EIGEN_MATH_FUNCTIONS_ZVECTOR_H</span></div>
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